The Penultimate Chain End Effect

The copolymerization equation was derived under the assumption that the probability for the addition of a monomer to the growing chain is determined only by the last monomeric unit. With highly polar monomeric units, however, the penultimate chain end may be expected to have an influence (penultimate effect). Consequently, instead of one equation for the rate, for example, of the process —MJ -h there are 

Since equations can be defined analogously for all eight possible processes, a total of four reactivity ratios will result  

This influence by the penultimate chain end can considerably modify the reactivity ratio (Table 22-4). The effect is particularly strong with monomers containing very polar groups near the main chain, and it is probably also responsible for the fact that the product of the conventionally determined reactivity ratios in the free radical copolymerization of ethylene with different monomers is sometimes greater than one (Table 22-5). 

In order to grasp the influence of the penultimate chain end on, for example. Mi, it is necessary to carry out very exact experiments at low ratios of [Mi]/[M2]. In addition, all other influences, such as that of the medium, must be excluded. Equation (22-42) becomes essentially simpler, however, when one of the two monomers does not unipolymerize (r2 = r 2 = 0), as, for example, is the case with hexafluoroacetone. 

The sequence distributions are far more sensitive to the reactivity ratios. In analogy to the derivation of the sequence distribution in normal copolymerization, we obtain 

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The influence of the penultimate member of the growing polymer chain (what is called the penultimate effect) has been often discussed as a cause of deviations from the simple copolymerization equation, especially in the case of strongly polar monomers. Very accurate experiments at very low monomer ratios must be carried out to establish such influences and to correspondingly modify the simple copolymerization equation. However, the penultimate chain end effect can often be better explained by the formation of CT complexes (see Figure 22-11). In this case, the CT complexes function as third monomer. 

In free radical copolymerizations, all the assumptions summarized in Section 22.1.1 are generally valid, i.e., bimolecular propagation mechanism, absence of the penultimate chain end effect or depolymerization, high degree of polymerization, and identity of overall and effective concentrations. Deviations were discussed in Sections 22.4.2 and 22.4.5. Table 22-3 contains the reactivity ratios for the free radical copolymerization of some monomer pairs that behave normally. 

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